128 PHENOMENA, ATOMS, AND MOLECULES 



peratures, and then by subtracting this from the observed heat loss at the 

 higher temperatures it was possible to find the energy that was carried from 

 the filament by the dissociation (or association) that occurred. A portion 

 of the data obtained in this way with a filament of 0.0706 mm. diameter at 

 a series of different pressures is given in Figure i.^ 



At temperatures from 2000° to 2400° K. more than twice as much heat 

 is carried in this way from the filament in hydrogen at 50 mm. pressure as 

 at 760 mm., but data beyond the range included in the diagram show that 

 this ratio falls to 1.55 at a filament temperature of 3400° K. At pressures 

 still lower than 50 mm. the heat loss does not continue to increase as the 

 pressure is lowered, but calculation shows that this is due to the fact that 

 the free path of the gas molecules is no longer negligible compared with the 

 diameter of the wire so that there is a "concentration drop" of the modified 

 hydrogen at the surface of the wire analogous to the temperature drop dis- 

 covered by Smoluchowski. 



The marked increase in heat loss as the pressure was lowered proved 

 that the heat was carried from the filament by a dissociation of the 

 hydrogen into atoms. In fact, the amount of the increase was in quantitative 

 agreement with a mathematical theory of the effect based on an assumed 

 dissociation. 



When the pressure was lowered to 10, i.i, and 0.2 mm. the heat loss 

 decreased with decreasing pressure (Figure i), and decreased much more 

 rapidly at the high temperatures than at the lower ones, so that finally 

 (at 0.21, 0.04, and 0.015 mm.) it became independent of the filament tem- 

 perature at temperatures above 2600° K. This indicates that the dissocia- 

 tion under these conditions is nearly complete, so that the rate of dis- 

 sociation, which determines the heat loss, is limited only by the rate at 

 which the molecules strike the surface of the wire. Quantitative calculations 

 based on the kinetic theory confirmed this conclusion. 



By means of these theoretical considerations it was possible to determine 

 the degree of dissociation and the heat of the reaction by which atoms com- 

 bine to form molecules. The results that were published in 191 5 gave 

 90,000 calories as the heat of combination of 2 grams of hydrogen atoms 

 at constant pressure and at 3000° K. The degree of dissociation,^ x, ex- 

 pressed as the fraction of the molecules which have been dissociated, was 

 found to be, at atmospheric pressure, 0.00165 at 2000° K., 0.0109 at 

 2400° K., and 0.0421 at 2800° K, 



Since these experiments were made, more accurate data for determin- 

 ing the temperatures of tungsten filaments have come into use. G. N. Lewis 



"* Langmuir and Mackay, Jour. Amer. Chem. Soc, 36. 1708 (1914). 

 'Langmuir, Ibid., 37, 417 (1915) ; 38, ii45 fiQi^)- 



